The present invention relates to a method for automated calibration of a Stratigraphic Forward Modelling (SFM) tool to available geological input data using a Neighborhood Algorithm (NA) with explicit escape clauses.
Calibration of a SFM tool refers to the process of obtaining a SFM that honors a given set of geological input data constraints and uncertainties, which cannot be imposed directly as input parameters to the SFM tool.
Cross and Lessenger disclose in U.S. Pat. No. 6,246,963 a SFM tool which inverts a stratigraphic/sedimentologic forward model with simultaneous multi-parameter inversion or other mathematical optimization techniques, such that forward model predictions are forced to obtain best match with observations. A disadvantage of this known SFM tool is that it has a natural tendency to converge to a single minimum. In addition to the focus on finding a single best solution (i.e. global minima) the 2D approach of the forward model is another main limitation of this known SFM tool.
This and other SFM prior art references are listed at the end of this specification.
Throughout other parts of this specification references to the listed prior art references are abbreviated by indicating the name of one or more authors and the year of publication. For example, a reference in the following paragraph to the listed prior art reference presented by Paola, C., 2000, Quantitative models of sedimentary basin filling: Sedimentology, v. 47, p. 121-178 is abbreviated as (Paola, 2000).
Stratigraphic Forward Modelling (SFM) tools are numerical, process-based software that aim to simulate tectonic and sedimentary processes controlling stratigraphic architecture (Paola, 2000). These tools can be classified according to the processes affecting sediment production, transport and deposition that they simulate, as well as the degree of the simplifications of these processes (Watney et al., 1999). SFM have been widely used to understand and illustrate controls on stratigraphy for a variety of sedimentary environments (Paola, 2000; Prather, 2000; Kubo et al., 2005; Burgess et al., 2006; Burgess and Steel, 2008; Williams et al., 2011). Currently, there are a variety of SFM used in the context of hydrocarbon exploration, for building basin models or to help in predicting reservoir presence and characteristics, such as DIONISOS (Granjeon, 1996; Joseph et al., 1998; Granjeon and Joseph, 1999), SEDSIM (Wendebourg and Harbaugh, 1996; Griffiths et al., 2001), or SEDFLUX (Syvistski and Hutton, 2001; Hutton and Syvistki, 2008).
Using SFM tools to describe local geology while systematically honoring given input data constraints (Lawrence et al., 1990; Shuster and Aigner 1994; Granjeon and Joseph, 1999), and understanding the sensitivities of these SFM models to input parameters difficult to infer directly from subsurface data (such as initial bathymetry, input sediment composition, rates of fluvial discharge, or transport efficiency parameters) is an “inverse problem”. Solving the SFM inverse problem is very challenging because: a) the SFM are not linear processes hence inversion is non-linear also, typically exhibiting very complex multi-modal error functions; b) SFM used for hydrocarbon exploration problems are often large-scale and large timescale, with significant computing resources required, and feature many unknowns; c) assessing the sensitivity of geological models to unknown parameters is non-trivial, and d) solutions are fraught with uncertainty due to sparse or imperfect data as well as imperfect modeling (SFM).
The most straightforward conventional approach to calibrate SFM tools is by manual trial and error. This approach has been widely applied (Euzen et al., 2004; Wijns et al., 2004; Warrlick et al., 2008; Teles et al., 2008; Hasler et al., 2008; Gratacos et al., 2009), and is included in U.S. Pat. No. 5,844,799 by Joseph et al., (1998). Manual trial and error is time consuming, prone to subjective user bias, and hence may not lead to optimal solutions. Some automatic inversion approaches to the calibration of SFM have been also employed; these are based on quantifying the degree to which existing models are consistent with the input data constraints using an objective- or error function, and iteratively testing new models aiming to minimize the error function evaluation. Such approaches mostly differ in the specifications of the error function and in the procedure to propose new models:
1) Lessenger and Cross (1996) used a deterministic gradient-descend method to invert 2D synthetic data using a SFM that predicts distributions of fluvial/coastal plain through shallow shelf facies tracts.
2) Cross and Lessenger (1999 and 2001) developed and patented, by means of the earlier described U.S. Pat. No. 6,246,963, an inversion algorithm based on gradient descent coupled to a 2D forward model of siliciclastic through marine shelf environments, and applied it to a 2D outcrop-based example. They incorporated into the solution an explicit method to escape local minima based on generating a coarse linear search independently for each parameter (other parameters being held constant) once every few iterations; referred to as Lerche inversion algorithm. As indicated earlier, the 2D approach of the forward model and the focus on finding a single best solution (i.e. global minima) are the main limitations of this known technique.
3) Charvin et al., (2009a and b) developed an inversion method based on a Markov-Chain Monte-Carlo method. They applied this method to the inversion of 2D synthetic data and outcrop data (Charvin et al., 2011) using a model of wave-dominated shallow-marine deposits.
4) Bornholdt et al., (1999) used a genetic algorithm to invert for 2D data in a carbonate margin. Genetic algorithms are similar to the neighborhood algorithm used in the present invention, in that they select only the best models to generate the next iteration of models. However, the next generation of models in genetic algorithms is based on cross-over and mutation from the best models so far, whereas in neighborhood algorithms the new models are simply drawn from the neighborhoods of the best models.
5) Sharma (2006), Imhof and Sharma (2006 and 2007), and Sharma and Imhof (2007) applied the neighborhood algorithm (NA) from Sambridge (1999a, 1999b), which is a direct-search optimization method. At each iteration of the original NA algorithm, the all-time best Nr models are identified, and each such model spawns Ns new models in its neighborhood; the neighborhoods are defined by the Voronoi tessellation of the ensemble of models and the sampling thereof is random. The new models are added to the current ensemble, the Voronoi tessellation is updated, and the whole process is repeated for several iterations. Sharma (2006) and Sharma and Imhof (2007) inverted the results of a laboratory flume experiment simulating a deltaic system honoring measured sediment thickness. Imhof and Sharma (2006 and 2007) inverted a delta calibrated by bedding attitude constraints derived from real seismic. In both cases, the SFM they used was based on a generalized diffusion with flux depending on topographic gradient but without the capability to differentiate lithologies. In order to mitigate the tendency of the original NA to become trapped by local minima, Imhof and Sharma (2006) and (2007) introduced the following modification: at each generation, a fraction of newly generated models are sampled around random models, instead of being sampled in the neighborhood of the best models so far.
There is a need to modify an evolutionary-genetic algorithm such as the original neighborhood algorithm (NA) by Sambridge (1999a) for calibration of stratigraphic forward models to data constraints. The original NA algorithm has been tested in the past for inverting SFM (Imhof and Sharma, 2006; 2007; Sharma, 2006; Sharma and Imhof, 2007). This original NA algorithm tends to be strongly attracted to a single minimum, which undermines its efficiency in the presence of very complex or multimodal error functions, as is common in SFM. One approach to mitigate this tendency is to mix subset of best models with a subset of totally random models, irrespective of their error values, as proposed by Imhof and Sharma (2006 and 2007); however this mechanism undermines the efficiency of the original NA algorithm because of the pure randomization, while not preventing oversampling of low-error regions, which tends to trap the algorithm very few local minima.
In summary, because geology is very complex, realistic process-based Stratigraphic Forward Modeling (SFM) models are necessarily complex too. SFM are directly controlled by parameters describing the geological processes simulated (i.e. input bathymetry, sediment supply rate, etc.); but in some cases it is also useful that these models are calibrated to available data such as seismic data and well data or other types of geological prior information, that cannot be used directly as input parameters for the SFM. This calibration can be achieved by using automatic inversion algorithms.
The SFM use approximations to the real processes governing sediment production, transport and sedimentation; and calibration data are comparatively sparse, uncertain, and often measured at different scales than the model prediction scales. Therefore, the distribution of admissible solutions to the inversion problem is typically multimodal because the models cannot predict with complete accuracy. This means that classical optimization techniques may miss some of the potential solutions; hence a multimodal approach is called for, such as evolutionary or genetic algorithms. Still, neighborhood search techniques, even multimodal, can get trapped by local minima, such techniques can waste significant modeling cycles oversampling local minima in an attempt to refine potential solutions and lower the error a bit further, instead of exploring for other potential new solutions—this is known as the “exploitation vs exploration” dilemma in optimization.
There is a need for a new approach to inhibit the tendency of conventional genetic or evolutioany algorithms such as the neighborhood algorithm (NA), to being attracted to a single minimum by identifying local minima and admissible solutions.